First lady taking break on mountain (7)
I believe the answer is:
everest
'mountain' is the definition.
(Mount Everest)
'first lady taking break' is the wordplay.
'first lady' becomes 'eve' (Biblical first woman).
'taking' means one lot of letters go next to another.
'break' becomes 'rest' (a rest is taking a break).
'eve'+'rest'='EVEREST'
'on' acts as a link.
(Other definitions for everest that I've seen before include "Himalyan peak" , "Huge achievement - highest climb" , "Where Hillary was" , "Himalayan peak" , "The world's highest mountain" .)